journal article·2026-05-02

On size effect and scaling behavior of ferritic steels in and near the ductile-brittle transition region

Sreten Mastilovic, Branislav Djordjevic, Aleksandar Sedmak

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Abstract

The stochasticity of fracture toughness of ferritic steels in the ductile-brittle transition (DBT) region arises primarily from aleatory uncertainty. Key micromechanical aspects include a Griffith microcrack nucleation by a breakage of the critical second-phase particle, randomly located ahead of the crack front, triggering an unstable propagation leading to a catastrophic failure. The scaling-based, weakest-link approach, proposed recently for the size effect modeling across the DBT region, was founded on the two-parameter Weibull distribution. This approach is further developed in this article to improve the physical robustness and flexibility of the two-step-scaling (2SS) procedure and to render the comparison with the standard Master Curve (MC) method more transparent. Specifically, the original 2SS method is enhanced by adding a lower limit on fracture toughness, resulting in a three-parameter Weibull (3P-W) distribution. Well-known datasets, corresponding to specimens of various sizes taken from a single segment of a reactor-pressure-vessel forging 22NiMoCr37, are analyzed to explore the reliability of the 2SS predictions. The empirical 2SS method is compared with the standard MC method, demonstrating its application flexibility and clarifying their relationship. Additionally, the proposed 3P-W 2SS variant incorporates a predetermined safety factor to enable a conservative assessment of fracture toughness.
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Research context

OpenAlex topics: High Temperature Alloys and Creep · Fatigue and fracture mechanics · Hydrogen embrittlement and corrosion behaviors in metals

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

University of Belgrade - Institute for Multidisciplinary Research

Innovation Center of Faculty of Mechanical Engineering

University of Belgrade

References (53)

Show source-provided references
1. 10.1080/0001873030074151810.1080/00018730300741518 ↗
2. Alias DO, Perez Ipiña JE, Berejnoi C (2021) Analysis of estimation of parameters in 3P-Weibull KJc distribution: Sample size effect. Engineering Transactions 69: 195–210.
3. Anderson TL (1991) Fracture Mechanics – Fundamentals and Applications. Boca Raton, FL: CRC Press.
4. Anderson TL Stienstra D Dodds RH (1994) A theoretical framework for addressing fracture in the ductile-brittle transition region. In: Landes JD McCabe DE Boulet JAM (eds) Fracture Mechanics: 24th Volume ASTM Special Technical Publication 1207. West Conshohocken PA: ASTM International 186–214.10.1520/STP13706S ↗
5. ASTM E1921-22a (2022) Standard test method for determination of reference temperature T0 for ferritic steels in the transition range. ASTM International West Conshohocken PA.
6. 10.1016/j.engfracmech.2025.11132610.1016/j.engfracmech.2025.111326 ↗
7. Berejnoi C Perez Ipiña JE (2016) Fracture toughness of ferritic steels in the Ductile-to-Brittle transition region. In: Alves LM (ed) Fracture Mechanics—Properties Patterns and Behaviours. Rijeka Croatia: InTech 83–101.10.5772/63410 ↗
8. 10.1590/1980-5373-MR-2015-051310.1590/1980-5373-MR-2015-0513 ↗
9. 10.1007/BF0266330210.1007/BF02663302 ↗
10. 10.1179/msc.1978.12.11.51110.1179/msc.1978.12.11.511 ↗
11. Diebold FX (2006) Elements of Forecasting, 4th ed. Boston, MA: Cengage.
12. 10.1016/j.engfracmech.2023.10971610.1016/j.engfracmech.2023.109716 ↗
13. 10.6028/jres.126.03610.6028/jres.126.036 ↗
14. 10.1016/j.tafmec.2017.05.01510.1016/j.tafmec.2017.05.015 ↗
15. 10.1016/S0013-7944(01)00067-410.1016/S0013-7944(01)00067-4 ↗
16. 10.1111/j.1460-2695.1993.tb00735.x10.1111/j.1460-2695.1993.tb00735.x ↗
17. 10.1016/0022-5096(68)90014-810.1016/0022-5096(68)90014-8 ↗
18. Kirk MT (2009) The Technical Basis for Application of the Master Curve to the Assessment of Nuclear Reactor Pressure Vessel Integrity. Washington, DC: U.S. Nuclear Regulatory Commission.
19. Lamon J (2016) Brittle Fracture and Damage of Brittle Materials: Statistical-Probabilistic Approaches. Amsterdam, Netherlands: Elsevier.
20. 10.1520/STP32565S10.1520/STP32565S ↗
21. Landes JD Shaffer DH (1980) Statistical characterization of fracture in the transition region. In Fracture Mechanics: Twelfth Conference ASTM STP 700: 368-382.10.1520/STP36981S ↗
22. Lucon E Scibetta M (2007) Application of advanced master curve approaches to the EURO fracture toughness dataset. Open Report of the Belgian Nuclear Research Centre SCK•CEN-BLG-1036. Mol Belgium.
23. 10.1177/105678951984847510.1177/1056789519848475 ↗
24. 10.1016/j.engfracmech.2017.05.01510.1016/j.engfracmech.2017.05.015 ↗
25. 10.1177/105678951038529410.1177/1056789510385294 ↗
26. Mastilovic S (2018a) Damage-fragmentation transition: Size effect and scaling behavior for impact fragmentation of slender projectiles. International Journal of Damage Mechanics 27(3): 201–217.
27. 10.2298/TAM171203007M10.2298/TAM171203007M ↗
28. 10.1016/j.engfailanal.2021.10583810.1016/j.engfailanal.2021.105838 ↗
29. 10.1016/j.engfailanal.2022.10675110.1016/j.engfailanal.2022.106751 ↗
30. 10.1016/j.engfracmech.2024.11033910.1016/j.engfracmech.2024.110339 ↗
31. 10.1016/j.mechmat.2007.10.00310.1016/j.mechmat.2007.10.003 ↗
32. McCabe DE (1993) A comparison of Weibull and βIc analyses of transition range data. In: Chona R (ed) Fracture Mechanics: 23rd Symposium ASTM Special Technical Publication 1189. West Conshohocken PA: ASTM International 80–94.10.1520/STP24265S ↗
33. 10.1007/BF0003535510.1007/BF00035355 ↗
34. 10.1016/0029-5493(87)90230-510.1016/0029-5493(87)90230-5 ↗
35. 10.1016/j.tafmec.2024.10449310.1016/j.tafmec.2024.104493 ↗
36. 10.3390/ma1206098210.3390/ma12060982 ↗
37. Raynaud P Kirk M Benson M et al. (2018) Important aspects of probabilistic fracture mechanics analyses. Technical Letter Report TLR-RES/DE/CIB-2018-01 U.S. Nuclear Regulatory Commission Washington DC.
38. 10.1016/0022-5096(68)90013-610.1016/0022-5096(68)90013-6 ↗
39. 10.1002/adma.20140102610.1002/adma.201401026 ↗
40. 10.1201/978142008744410.1201/9781420087444 ↗
41. 10.1016/j.mechmat.2024.10505510.1016/j.mechmat.2024.105055 ↗
42. 10.1016/j.engfracmech.2024.10991710.1016/j.engfracmech.2024.109917 ↗
43. 10.1016/j.tafmec.2024.10459810.1016/j.tafmec.2024.104598 ↗
44. Stauffer D, Aharony A (1992) Introduction to Percolation Theory. London, UK: Taylor & Francis.
45. 10.1016/0013-7944(85)90167-510.1016/0013-7944(85)90167-5 ↗
46. Wallin K (1991) Statistical modelling of fracture in the ductile to brittle transition region. In: Blauel JG Schwalbe K-H (eds) Defect Assessment in Components: Fundamentals and Applications. vol. 9 Birchwood UK: EGF/ESIS 415–445.
47. 10.1504/IJMPT.1999.03627610.1504/IJMPT.1999.036276 ↗
48. 10.1016/S0013-7944(01)00071-610.1016/S0013-7944(01)00071-6 ↗
49. 10.1007/978-94-009-6146-3_3210.1007/978-94-009-6146-3_32 ↗
50. Weibull W (1939) A statistical theory of the strength of materials. Generalstabens Litografiska Anstalts Förlag Stockholm.
51. 10.1115/1.401033710.1115/1.4010337 ↗
52. 10.1016/j.tafmec.2024.10481510.1016/j.tafmec.2024.104815 ↗
53. 10.1016/j.tafmec.2022.10338210.1016/j.tafmec.2022.103382 ↗